双边黑洞大叠加态的量子态
Null states from large superpositions of two-sided black holes
摘要：
AdS/CFT对应的一个标准见解是，体态几何的某些方面被编码在其双边界态的纠缠结构中。由于纠缠不是线性的量子可观测量，这意味着引力的量子理论中的几何也不应该是线性的可观测量。这允许具有不同几何形状的状态之间的线性依赖性。我们探索具有简单几何对偶的某些状态之间的线性依赖关系：由热场双态的$n$副本组成的状态以及通过排列$n$右侧而从该副本获得的状态。有$n!$这样的状态，都是不同几何的对偶。我们推导出一个这样的状态和其他的线性组合之间的最大保真度的表达式，并看到，这种保真度接近1的黑洞的数量$n$增加。我们还考虑了获得一个单一的热场双态的可能性，作为一个叠加态的拓扑结构不连接两个未跟踪的边的部分跟踪。我们推导出的温度场的双重状态和这种部分的痕迹之间的保真度的下限和评论的概念上的影响，这种状态的存在。
英文摘要：
A standard insight of the AdS/CFT correspondence is that some aspects of the geometry of a bulk state are encoded in the entanglement structure of its dual boundary state. As entanglement is not a linear quantum observable, this means that geometry in a quantum theory of gravity should likewise not be a linear observable. This allows for linear dependencies between states with distinct geometries. We explore linear dependencies between certain states with simple geometric duals: states made up of $n$ copies of a thermofield double state and the states obtained from this one by permuting the $n$ right hand sides. There are $n!$ such states, all dual to distinct geometries. We derive expressions for the maximum fidelity between one such state and a linear combination of the others, and see that this fidelity approaches 1 as the number $n$ of black holes increases. We also consider the possibility of obtaining a single thermofield double state as the partial trace of a superposition of states whose topology does not connect the two untraced sides. We derive lower bounds for the fidelity between the thermofield double state and such partial traces and comment on the conceptual implications of the existence of such states.
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